Abstract

The Dirac equation is solved for quaternionic potentials, iV0 + jW0 (). The study shows two different solutions. The first one contains particle and anti-particle solutions and leads to the diffusion,tunneling, and Klein energy zones. The standard solution is recovered taking the complex limit of this solution. The second solution, which does not have a complex counterpart, can be seen as a V0-antiparticle or |W0|-particle solution.

The authors gratefully thank the CNPq (Stefano De Leo) and CAPES (Sergio Giardino) for the financial support and an anonymous referee for his very useful suggestions and observations. We also thank the referee for having stimulated the final discussion presented in our conclusions.